Number of unlabelled graphs with given number of triangles

Counts for the numbers of unlabelled graphs with
n vertices, e edges and t triangles.

I know of no other source for these counts.
The Encyclopedia of Integer Sequences lists the number of graphs
on n vertices in sequence
A000088
and the number of graphs on n vertices with e edges in sequence
A008406.
See also
Brendan McKay,
Gordon Royle
and Durango Bill.